Large-volume open sets in normed spaces without integral distances

Sascha Kurz; Valery Mishkin

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arXiv · 1401.8174

Large-volume open sets in normed spaces without integral distances

Sascha Kurz·Valery Mishkin

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Abstract

We study open sets $\mathcal{P}$ in normed spaces $X$ attaining a large volume while avoiding pairs of points at integral distance. The proposed task is to find sharp inequalities for the maximum possible $d$-dimensional volume. This problem can be viewed as an opposite to known problems on point sets with pairwise integral or rational distances.

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BibTeX RIS

Sascha Kurz, Valery Mishkin. 2014-01-31. Large-volume open sets in normed spaces without integral distances. https://arxiv.org/abs/1401.8174

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